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# A, B and C Can Reap a Field in 15 3 4 Days; B, C and D in 14 Days; C, D and a in 18 Days; D, a and B in 21 Days. in What Time Can A, B, C and D Together Reap It? - Mathematics

Course
ConceptTime and Work

#### Question

AB and C can reap a field in $15\frac{3}{4}$ days; BC and D in 14 days; CD and A in 18 days; DA and B in 21 days. In what time can ABC and D together reap it?

#### Solution

$\text{ Time taken by } \left( A + B + C \right) \text{ to do the work } = 15\frac{3}{4} \text{ days } = \frac{63}{4} \text{ days }$
$\text{ Time taken by } \left( B + C + D \right) \text{ to do the work = 14 days}$
$\text{ Time taken by } \left( C + D + A \right) \text{ to do the work = 18 days }$
$\text{ Time taken by } \left( D + A + B \right) \text{ to do the work = 21 days }$
$\text{ Now, }$
$\text{ Work done by } \left( A + B + C \right) = \frac{4}{63}$
$\text{ Work done by } \left( B + C + D \right) = \frac{1}{14}$
$\text{ Work done by } \left( C + D + A \right) = \frac{1}{18}$
$\text{ Work done by } \left( D + A + B \right) = \frac{1}{21}$
$\therefore \text{ Work done by working together } = \left( A + B + C \right) + \left( B + C + D \right) + \left( C + A + D \right) + \left( D + A + B \right)$
$= \frac{4}{63} + \frac{1}{14} + \frac{1}{18} + \frac{1}{21}$
$= \frac{4}{63} + \left( \frac{9 + 7 + 6}{126} \right) = \frac{4}{63} + \frac{22}{126}$
$= \frac{4}{63} + \frac{11}{63} = \frac{15}{63}$
$\therefore \text{ Work done by working together } = 3\left( A + B + C + D \right) = \frac{15}{63}$
$\therefore \text{ Work done by } \left( A + B + C + D \right) = \frac{15}{63 \times 3} = \frac{5}{63}$
$\text{ Thus, together they can do the work in } \frac{63}{5} \text{ days or } 12\frac{3}{5} \text{ days } .$

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#### APPEARS IN

Solution A, B and C Can Reap a Field in 15 3 4 Days; B, C and D in 14 Days; C, D and a in 18 Days; D, a and B in 21 Days. in What Time Can A, B, C and D Together Reap It? Concept: Time and Work.
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